Let's say Congress passed, and the President signed a law mandating a 30-hour work week. Anything worked over 30 hours a week would be subject to overtime pay requirements like we do now with the 40 hour work week.
How would this actually work?
Would hourly wages remain the same so now you have to make due on 10 hours less a week in earning? Or would wages get adjusted so if you were making $500/week working 40 hours you'd still earn $500/week working 30 hours?
This would essentially be a 12.5% pay raise for all wage earners, if nothing else changed. If the expected 40 hour pay were compressed into the 30 hour week, and the person worked the additional 10 hours, it would be a 37.5% pay raise. I don't think that is a likely scenario.
The economic question to answer is how much production would be lost if the work week were cut by 25%. A manager has a few options. The first is to pay the money and absorb the difference. Another option is to hire more people and limit them to 30 hrs. This keeps the payroll down, but increases costs, especially the intangible costs of managing more people. Unless production increases by about 25%, the business becomes less efficient.
The idea of shorter work weeks as a method of increasing employment has been around for a long time. The problem with the idea is that in times of high unemployment, many businesses are on the margin of profitability. Any decrease in efficiency will push them into a money losing situation. This leads to layoffs and business closings, which is the opposite of the policy's goal.
I think it could conceivably reduce "unemployment" in the sense of more people having some sort of job but I don't see how it would increase the aggregate hours worked or wages (if anything the inefficiencies created would depress these) so you'd be spreading the same amount (or less) money around to more people. Not sure that's a good thing.
It is not a good thing. Using more people to do the same amount of work is unavoidably less efficient. The money lost through these inefficiencies would be better spent on investment in training and economic infrastructure. It's the old "teach a man to fish and then build a pier to fish off of" thing.